Double Helicity Asymmetry in ${\pi }^0$ Production at Midrapidity in Polarized $p+p$ Collisions at $\sqrt{s}=510$ GeV

PHENIX measurements are presented for the cross-section and double-helicity asymmetry ($A_{LL}$) of inclusive ${\pi }^0$ production ($A_{LL}^{{\pi }^0}$) at midrapidity from $p+p$ collisions at $\sqrt{s}=510$ GeV from data taken in 2012 and 2013 at the Relativistic Heavy Ion Collider (RHIC). The next-to-leading order (NLO) perturbative QCD (pQCD) calculation agrees excellently with the presented cross-section result. The $A_{LL}^{{\pi }^0}$ follows an increasingly positive asymmetry as functions of $p_T$ and $\sqrt{s}$ at the fixed $x_T$. The latest global analysis results, which support the positive spin contribution of gluon ($\mathrm{\Delta }G$), agrees excellently with the presented asymmetry result. The asymmetry result extends the experimental sensitivity to the previously unexplored $x$ region down to $x\sim 0.01$ and provides additional constraints on $\mathrm{\Delta }G$.